# Problem with RHP zero in transfer function

I have a transfer function with a RHP zero in $$s=+1$$, and I am trying to show in Matlab thath this limitation is present. In particular, initially I had a MIMO system, which I decoupled and then I started doing this analysis on the two separate SISO system that came out of the decoupling.

My code is the following:

s = tf('s');
G = [2/(s+1) 3/(s+2);1/(s+1) 1/(s+1)];

d_12 = -(G(1,2)/G(1,1));
d_21 = -(G(2,1)/G(2,2));
D_simp = [1 d_12;d_21 1];  %decoupler
F1 = G*D_simp;

k1 = 5;
k2 = 2;
k3 = 50;

loop1 = loopsens(F1(1,1),k1/s);
loop2 = loopsens(F1(1,1),k2/s);
loop3 = loopsens(F1(1,1),k3/s);

figure;
bodemag(loop1.Ti,'r',loop2.Ti,'b',loop3.Ti,'g'),grid
figure;
bodemag(loop1.Si,'r',loop2.Si,'b',loop3.Si,'g'),grid

where I am trying to increase the bandwidth of the system by increasing the gain.

The expected result is that if I increase the bandwidth , I should have worse performances as the bandwidth increases, but what happen is exaclty the opposite:

can somebody please help me solve this problem?

## 1 Answer

This is because for all three of of your choices for the gain the closed loop system is unstable. Namely, for just an integrator as controller the gain should be below 1.5 in order for the closed loop system to be stable and all of your gains are above that.